🧮 algebra

1. The problem asks to create the graph for part B of problem 1. 2. Since the original problem is not provided here, I will assume part B involves graphing a function or equation g

1. **State the problem:** We need to find the expansion of the expression $ (8a + 3b)^2 $. 2. **Formula used:** The square of a binomial $ (x + y)^2 $ is given by the formula:

1. **State the problem:** We need to find the sum of the two polynomials $x^2 + 3x - 9$ and $4x^2 - 6x + 1$. 2. **Formula and rules:** When adding polynomials, combine like terms.

1. **State the problem:** Simplify the expression $\left(w^{-3}\right)^{-5}$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents

1. **State the problem:** We need to find the product of the binomials $ (7x - 3)(5x + 2) $. 2. **Formula used:** To multiply two binomials, use the distributive property (FOIL met

1. **State the problem:** Simplify the expression $$\frac{k^6 p^3 t^5}{k r^2 t^4}$$ assuming no denominator equals zero. 2. **Recall the rules:** When dividing powers with the same

1. **State the problem:** Simplify and understand the expression $$4.1h\left(\sqrt[3]{x^{2} + 3x + 4}\right)$$ but with the numerator inside the cube root changed from 3 to 1, so t

1. **State the problem:** Match each algebraic expression to its corresponding graph or simplified form.

1. **State the problem:** Find the value of $\left(3x^{2}y^{-5}\right)^{3}$. 2. **Recall the exponent rules:** When raising a product to a power, raise each factor to that power:

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. The problem is to solve the equation $$\frac{2x+3}{4} = 5$$ for $x$. 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting lin

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **State the problem:** We need to find how many hours it takes for the moisture content to reduce from 42% to 14% if it decreases by 7% per hour. 2. **Formula and explanation:**

1. **State the problem:** We know 752 tickets were sold with the ratio of adult to children tickets as 3:1. We need to find the number of adult and children tickets sold. 2. **Use

1. **State the problem:** Find the left and right x-intercepts, the axis of symmetry, and the vertex of the quadratic function $$y = -(x + 1)(x - 5)$$. 2. **Find the x-intercepts:*

1. **Simplify each expression and leave in fraction and exponent form with positive exponents.** ---

1. **State the problem:** We need to graph the quadratic function $$y = -\frac{1}{2}(x - 3)^2 + 5$$ and understand its shape and key features. 2. **Formula and important rules:** T

1. **State the problem:** We are given the quadratic function $y = -x^2 - 2x + 4$ and need to find the vertex, axis of symmetry, direction the parabola opens, domain, and range. 2.

1. **State the problem:** Find the axis of symmetry, vertex, y-intercept, and x-intercepts of the parabola given by the equation $y = 3x^2 + 12x + 9$. 2. **Axis of symmetry formula

1. The problem asks to identify which inequality corresponds to a graph of a downward-opening parabola with x-intercepts near $x=2$ and $x=4$, vertex near $(3,5)$, and shading belo

1. **Stating the problem:** We want to find a quadratic function $f(x) = ax^2 + bx + c$ that fits the given temperature data over time without using the second difference formula.